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Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population
Atushi Ishikawa1, Shouji Fujimoto1, Arturo Ramos2
1Department of Economic Informatics, Kanazawa Gakuin University, Kanazawa 920-1392, Japan.
Abstract:
We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat's law, and the non-Gibrat's property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat's property, and quasi-time-reversal symmetry.
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